The Toyota Corolla and Mazda 3 are the better choices in this category. They're both bigger than the Toyota Yaris, and still get good gas mileage. That, and I agree with you: they both look a heck of a lot better.
The Corolla will get better mileage than the 3, but the 3 is more fun to drive and much sportier (particularly if you go for the Speed option, but that takes the price over $20,000).
Other 4-Door models you may want to consider in the sub-$20,000 range are other compact cars like these:
Chevrolet Cobalt
Dodge Caliber
Ford Focus
Honda Civic
Hyundai Elantra
Jeep Compass
Kia Spectra
Mitsubishi Lancer
Nissan Sentra
Saturn Astra
Subaru Impreza
Suzuki Forenza
Suzuki Reno
Volkswagen Jetta
Volkswagen Rabbit
They're all similar in size, performance, price, and available options to the Corolla and 3, but some are better than others. The Volkswagens have the best interiors, while the Hyundai, Kia, and Suzuki offer the most standard equipment and the lowest prices. The Ford offers the lowest price overall (just $14,200), which leaves room for the options you want rather than standard equipment you don't need. The sportiest of the bunch are the aforementioned Mazda 3, plus the Volkswagen Rabbit, Mitsubishi Lancer, and Subaru Impreza. The Mitsubishi and Subaru also offer All-Wheel Drive if you live in a place that gets snow and ice like I do. In terms of long-term reliability, Honda, Subaru, and Toyota have always been the best, with Ford and Suzuki close behind.
I hope this has answered your question. If you have any more, please feel free to ask.